解题方法
1 . 如图所示,在平面直角坐标系
上放置一个边长为1的正方形PABC,此正方形PABC沿
轴滚动(向左或向右均可),滚动开始时,点P位于原点处,设顶点
的纵坐标与横坐标的函数关系是
,该函数相邻两个零点之间的距离为m.
(1)写出m的值并求出当
时,点P运动路径的长度
;
(2)写出函数
的表达式;研究该函数的性质并填写下面表格:
(3)试讨论方程
在区间
上根的个数及相应实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee82283f06cedef32eb15b87964f5d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/208836dfd77253efa91e9956d0d769a7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/5/c65f43f5-df1a-46a4-b0c6-b9a4320af870.png?resizew=162)
(1)写出m的值并求出当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f52db3046e7c92b3a7fdd6c34657663.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)写出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cc61760a5002a5e387a33c8b768b292.png)
函数性质 | 结论 |
奇偶性 | |
单调性 | |
零点 | |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36f12bc35b1aa8d82897a2ac6acaaabe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a23270dc14c9cea8b127f17f554b8e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2 . 已知点
在幂函数
的图像上.
(1)求
的表达式;
(2)设
,求函数
的零点,推出函数
的另外一个性质(只要求写出结果,不要求证明),并画出函数
的简图.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4be51cbfd93024c4b5b38bb52d103b13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b29a7faa14a6e09d0db2d04f4ced03.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8221c8390d24c3d9dcd359118bb4c430.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dc6e69ad1a27916fb5c3d5901ded134.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dc6e69ad1a27916fb5c3d5901ded134.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dc6e69ad1a27916fb5c3d5901ded134.png)
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3 . 画出函数
的图象,并写出它的单调区间和零点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a415bcc451b8d4ab4e563b1bd81e84b.png)
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名校
4 . 已知
,
.
(1)写出
的解析式与定义域;
(2)画出函数
的图像;
(3)试讨论方程
的根的个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/addec13c8cdc30dcad020d5bed77e5c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8bfb925d9da2d4057aa6a97e354834b.png)
(1)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5790d5181783c15fd46d95bf18b796f0.png)
(2)画出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4add65345979e0b5b500c389be95b8e.png)
(3)试讨论方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b37937af4d650f37d683d23888a715e8.png)
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2013·上海浦东新·二模
5 . 设函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60637c4a50694a4a4bb1d1723b78e711.png)
(1)当
,画出函数
的图像,并求出函数
的零点;
(2)设
,且对任意
,
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60637c4a50694a4a4bb1d1723b78e711.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e368f1b7109436bb94f40363544ffec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/320786c30e758bda019f2f4f88224ff9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc70276e8bba4f3a519be50442f0f21c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/030805eebb5ad0a065f93bd6f652f687.png)
![](https://img.xkw.com/dksih/QBM/2013/4/26/1571198516207616/1571198521974784/STEM/b089c79e70b24419aad4e3f69492e8b7.png)
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